Over the past few months, the JC has reported that both schools wish to stop their policy of prioritising children who attend feeder schools. This has caused unrest among families with young children - especially those living in Hertfordshire, who are based too far away from Yavneh to guarantee a place.
"Last year, some kids were left waiting for months to find out where they were going to go, and it's only going to get worse," said Mr Rotenberg.
Mr Rotenberg explained that it was a "combination of factors" that led him and Rabbi Lister, who are acting under the newly-created Nekadma Trust, to launch their plans now - with a view to opening the free school in September 2017.
"When you add the concerns I get told as chair of Rosh Pinah to the constant JC attention, then hear what JCoSS and Yavneh are doing, it's not exactly rocket science," Mr Rotenberg said.
He said that while Yavneh served Hertfordshire, there was little on offer for families in Barnet who were not as Orthodox as the clientele at Hasmonean, but who did not necessarily align themselves to JCoSS' cross-communal ethos.
"If you look at mainstream Orthodox primary schools in Barnet - in reality, their pupils are all applying to Yavneh and JFS, neither of whom are in the borough," he said. "Now you have Yavneh saying it is only serving WD and Al postcodes. If you live in Finchley or Barnet, where are you going to go?"
If successful, Kedem would be the first Jewish secondary free school in London. Its application will be submitted to the Government in March, following a consultation period.
The project will be in partnership with Lilac Sky Outstanding Education Services, an educational agency which was called in to manage Rosh Pinah last year.
"Lilac Sky are experts in setting up schools from scratch," Mr Rotenberg said.
He explained that the school will offer a "truly integrated secular and Jewish Orthodox curriculum" under the auspices of the Chief Rabbi.
Mr Rotenberg said that he believed that Kedem would end up as a "Yavneh-sized school" - that is, with 150 pupils per year.
He added: "Our intent is not to create an abundance of empty seats. All we are trying to do is fulfil the demonstrable, desperate need of parents for a secondary school in Barnet. We are going to gauge interest from the community."
While Kedem's website declares it would be under the aegis of Chief Rabbi Ephraim Mirvis, a statement from his office indicated that it would be premature to claim his backing.
The Chief Rabbi, his office said, was "instinctively supportive of new proposals that will enhance opportunities for Jewish education across our community and would be pleased to meet with representatives of Kedem."
But it urged all those involved "to ensure that a comprehensive consultation process is in place".
